Anomalous percolation flow transition of yield stress fluids in porous media

Abstract

Yield stress fluid (YSF) flows through porous materials are fundamental to biological, industrial, and geophysical processes, from blood and mucus transport to enhanced oil recovery. Despite their widely recognized importance across scales, the emergent transport properties of YSFs in porous environments remain poorly understood due to the nonlinear interplay between complex fluid rheology and pore microstructure. Here, we combine microfluidic experiments and nonlinear network theory to uncover an anomalous, hierarchical yielding process in the fluidization transition of a generic YSF flowing through a random medium. Percolation of a single fluidized filament gives way to pathways that branch and merge to form a complex flow network within the saturated porous medium. The evolution of the fluidized network with the flowing fraction of YSF results in a highly nonlinear flow conductivity and reveals a novel dispersion mechanism, resulting from the rerouting of fluid streamlines. The identified flow percolation phenomenon has broad implications for YSF transport in natural and engineered systems, and provides a tractable archetype for a diverse class of breakdown phenomena.

The first open channel for yield-stress fluids in porous media

“…Additionally, we observe that decreasing the ratio leads to an increase in , in qualitative agreement with experiments (Waisbord et al. 2019). The reason for this behaviour can be explained by examining the arclength (defined as ) for the first open channel.…”

“…This behaviour is expected as h i of each edge decreases monotonically as φ increases (Torquato & Haslach 2002). Additionally, we observe that decreasing the ratio R s /L leads to an increase in ΔP c , in qualitative agreement with experiments (Waisbord et al 2019). The reason for this behaviour can be explained by examining the arclength (defined as L c = N i i ) for the first open channel.…”

“…Another complication on the yield-stress criterion might come from the dimensionality of the porous medium. In three-dimensional structures, the description of open channels as tubes might not be adequate, and the geometric quantities h i and i need to be chosen carefully (Waisbord et al 2019). Thus, for irregular porous media, the yielding criterion, and thus the expression related to the minimum pressure to open the first channel, should be modified.…”

“…2016; Waisbord et al. 2019) depends on the heterogeneous geometric characteristics and porosity of the porous medium, where is the volume fraction of the solid phase (Talon et al. 2013; Bauer et al.…”

“…In pressure-driven flows, the critical pressure drop ΔP c required to fluidize the yield-stress fluid and open the first channel (Chen, Rossen & Yortsos 2005;Hewitt et al 2016;Waisbord et al 2019) depends on the heterogeneous geometric characteristics and porosity 1 − φ of the porous medium, where φ is the volume fraction of the solid phase (Talon et al 2013;Bauer et al 2019;Chaparian & Tammisola 2021). Therefore, it is crucial to understand the relation between the yielding conditions and the structure of the porous medium, which will lead to predictive models for both the first open channel and ΔP c .…”